Meter electronics and methods for determining void fraction of gas

ABSTRACT

Meter electronics ( 20 ) for determining a void fraction of gas in a flow material flowing through a flow meter ( 5 ) is provided according to an embodiment of the invention. The meter electronics ( 20 ) includes an interface ( 201 ) for receiving a frequency response of the flow material and a processing system ( 203 ) in communication with the interface ( 201 ). The processing system ( 203 ) is configured to receive the frequency response from the interface ( 201 ), break out the frequency response into at least a gas frequency component and a fluid frequency component, and determine the void fraction of gas from the frequency response and one or more of the gas frequency component and the fluid frequency component.

The present application claims the benefit of PCT Patent Application No.PCT/US06/19597, entitled “Meter Electronics and Methods for DeterminingVoid Fraction of Gas”, filed on May 19, 2006, which claims benefit ofU.S. Provisional Patent Application No. 60/683,516, entitled “MeterElectronics and Methods for Determining Void Fraction of Gas”, filed onMay 20, 2005.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to meter electronics and methods fordetermining a void fraction of gas in a flow material flowing through aflow meter.

2. Statement of the Problem

It is known to use Coriolis mass flow meters to measure mass flow,density, and volume flow and other information of materials flowingthrough a pipeline as disclosed in U.S. Pat. No. 4,491,025 issued to J.E. Smith, et al. of Jan. 1, 1985 and Re. 31,450 to J. E. Smith of Feb.11, 1982. These flow meters have one or more flow tubes of differentconfigurations. Each conduit configuration may be viewed as having a setof natural vibration modes including, for example, simple bending,torsional, radial and coupled modes. In a typical Coriolis mass flowmeasurement application, a conduit configuration is excited in one ormore vibration modes as a material flows through the conduit, and motionof the conduit is measured at points spaced along the conduit.

The vibrational modes of the material filled systems are defined in partby the combined mass of the flow tubes and the material within the flowtubes. Material flows into the flow meter from a connected pipeline onthe inlet side of the flow meter. The material is then directed throughthe flow tube or flow tubes and exits the flow meter to a pipelineconnected on the outlet side.

A driver applies a force to the flow tube. The force causes the flowtube to oscillate. When there is no material flowing through the flowmeter, all points along a flow tube oscillate with an identical phase.As a material begins to flow through the flow tube, Coriolisaccelerations cause each point along the flow tube to have a differentphase with respect to other points along the flow tube. The phase on theinlet side of the flow tube lags the driver, while the phase on theoutlet side leads the driver. Sensors are placed at different points onthe flow tube to produce sinusoidal signals representative of the motionof the flow tube at the different points. The phase difference betweenthe two sensor signals is proportional to the mass flow rate of thematerial flowing through the flow tube or flow tubes. In one prior artapproach either a Discrete Fourier Transform (DFT) or a Fast FourierTransform (FFT) is used to determine the phase difference between thesensor signals. The phase difference, and a vibrational frequencyresponse of the flow tube assembly, are used to obtain the mass flowrate.

In one prior art approach, an independent reference signal is used todetermine a pickoff signal frequency, such as by using the frequencysent to the vibrational driver system. In another prior art approach,the vibrational response frequency generated by a pickoff sensor can bedetermined by centering to that frequency in a notch filter, wherein theprior art flowmeter attempts to keep the notch of the notch filter atthe pickoff sensor frequency. This prior art technique works fairly wellunder quiescent conditions, where the flow material in the flowmeter isuniform and where the resulting pickoff signal frequency is relativelystable. However, the phase measurement of the prior art suffers when theflow material is not uniform, such as in two-phase flows where the flowmaterial comprises a liquid and a solid or where there are air bubblesin the liquid flow material. In such situations, the prior artdetermined frequency can fluctuate rapidly. During conditions of fastand large frequency transitions, it is possible for the pickoff signalsto move outside the filter bandwidth, yielding incorrect phase andfrequency measurements. This also is a problem in empty-full-emptybatching, where the flow meter is repeatedly operated in alternatingempty and full conditions. Also, if the frequency of the sensor movesrapidly, a demodulation process will not be able to keep up with theactual or measured frequency, causing demodulation at an incorrectfrequency. It should be understood that if the determined frequency isincorrect or inaccurate, then subsequently derived values of density,volume flow rate, etc., will also be incorrect and inaccurate. Moreover,the error can be compounded in subsequent flow characteristicdeterminations.

In the prior art, the pickoff signals can be digitized and digitallymanipulated in order to implement the notch filter. The notch filteraccepts only a narrow band of frequencies. Therefore, when the targetfrequency is changing, the notch filter may not be able to track thetarget signal for a period of time. Typically, the digital notch filterimplementation takes 1-2 seconds to track to the fluctuating targetsignal. Due to the time required by the prior art to determine thefrequency, the result is not only that the frequency and phasedeterminations contain errors, but also that the error measurementencompasses a time span that exceeds the time span during which theerror and/or two-phase flow actually occur. This is due to the relativeslowness of response of a notch filter implementation.

The result is that the prior art flowmeter cannot accurately, quickly,or satisfactorily track or determine a pickoff sensor frequency duringtwo-phase flow of the flow material in the flowmeter. Consequently, thephase determination is likewise slow and error prone, as the prior artderives the phase difference using the determined pickoff frequency.Therefore, any error in the frequency determination is compounded in thephase determination. The result is increased error in the frequencydetermination and in the phase determination, leading to increased errorin determining the mass flow rate. In addition, because the determinedfrequency value is used to determine a density value (density isapproximately equal to one over frequency squared), an error in thefrequency determination is repeated or compounded in the densitydetermination. This is also true for a determination of volume flowrate, where the volume flow rate is equal to mass flow rate divided bydensity.

Therefore, the prior art suffers from an inaccuracy or loss ofmeasurement ability during two-phase flow conditions. In many flowapplications, it is possible to have air (or other gas) entrained in theflow material. One example is oil field production, wherein crude oilthat is pumped out of an oil well will likely contain air mixed in withthe crude oil. Other examples are entrained air in a liquid in a foodmanufacturing process. The entrained air typically exists as bubbles inthe flow liquid. The air bubbles can cause erroneous mass flow rates ina flow meter. It is highly desirable that a flow meter accuratelymeasure a mass flow rate of the flow liquid even with any amount ofentrained air mixed into the flow liquid. It is highly desirable that aflow meter accurately measure a mass flow rate of the flow liquid evenwhere the entrained air is fluctuating.

SUMMARY OF THE SOLUTION

The above and other problems are solved and an advance in the art isachieved through the provision of meter electronics and methods fordetermining a void fraction of gas in a flow material.

Meter electronics for determining a void fraction of gas in a flowmaterial flowing through a flow meter is provided according to anembodiment of the invention. The meter electronics comprises aninterface for receiving a frequency response of the flow material and aprocessing system in communication with the interface. The processingsystem is configured to receive the frequency response from theinterface, break out the frequency response into at least a gasfrequency component and a fluid frequency component, and determine thevoid fraction of gas from the frequency response and one or more of thegas frequency component and the fluid frequency component.

A method for determining a void fraction of gas in a flow materialflowing through a flow meter is provided according to an embodiment ofthe invention. The method comprises receiving a frequency response ofthe flow material, breaking out the frequency response into at least agas frequency component and a fluid frequency component, and determiningthe void fraction of gas from the frequency response and one or more ofthe gas frequency component and the fluid frequency component.

A method for determining a void fraction of gas in a flow materialflowing through a flow meter is provided according to an embodiment ofthe invention. The method comprises receiving a frequency response ofthe flow material, processing the frequency response with a notch filterthat substantially rejects one of a gas frequency component and a fluidfrequency component, and determining the void fraction of gas from thefrequency response and one or more of the gas frequency component andthe fluid frequency component.

A method for determining a void fraction of gas in a flow materialflowing through a flow meter is provided according to an embodiment ofthe invention. The method comprises receiving a frequency response ofthe flow material and filtering the frequency response with a firstfilter that substantially rejects the gas frequency component andsubstantially passes the fluid frequency component. The first filteroutputs the fluid frequency component. The method further comprisesfiltering the frequency response with a second filter that substantiallyrejects the fluid frequency component and substantially passes the gasfrequency component. The second filter outputs the gas frequencycomponent. The method further comprises determining the void fraction ofgas from the frequency response and one or more of the gas frequencycomponent and the fluid frequency component.

ASPECTS OF THE INVENTION

In one aspect of the meter electronics, the void fraction of gascomprises a void fraction of air.

In one aspect of the meter electronics, the interface includes adigitizer configured to digitize the frequency response.

In another aspect of the meter electronics, the processing system isfurther configured to receive a first sensor signal and a second sensorsignal from the flow meter, generate a ninety degree phase shift fromthe first sensor signal, and compute the frequency response using theninety degree phase shift.

In yet another aspect of the meter electronics, the processing system isfurther configured to receive a first sensor signal and a second sensorsignal from the flow meter, generate a ninety degree phase shift fromthe first sensor signal, and compute the frequency response using thefirst sensor signal and the ninety degree phase shift.

In yet another aspect of the meter electronics, the processing system isfurther configured to break out the frequency response by processing thefrequency response with one or more filters that substantially rejectone of the gas frequency component and the fluid frequency component.

In yet another aspect of the meter electronics, the processing system isfurther configured to break out the frequency response by processing thefrequency response with a notch filter that substantially rejects one ofthe gas frequency component and the fluid frequency component.

In yet another aspect of the meter electronics, the processing system isfurther configured to break out the frequency response by filtering thefrequency response with a first filter that substantially rejects thegas frequency component and substantially passes the fluid frequencycomponent and filtering the frequency response with a second filter thatsubstantially rejects the fluid frequency component and substantiallypasses the gas frequency component. The first filter outputs the fluidfrequency component and the second filter outputs the gas frequencycomponent.

In yet another aspect of the meter electronics, the processing system isfurther configured to break out the frequency response by processing thefrequency response with a low-pass filter, with a low-pass cut-offfrequency of the low-pass filter being substantially above the fluidfrequency component and with the low-pass filter substantially passingthe fluid frequency component and substantially rejecting the gasfrequency component, and processing the frequency response with ahigh-pass filter, with a high-pass cut-off frequency of the high-passfilter being substantially below the gas frequency component and withthe high-pass filter substantially passing the gas frequency componentand substantially rejecting the fluid frequency component. The low-passfilter outputs the fluid frequency component and the high-pass filteroutputs the gas frequency component.

In yet another aspect of the meter electronics, the processing system isfurther configured to determine the void fraction of gas by calculatingan overall density from the frequency response, calculating a fluidcomponent density from the fluid frequency component, calculating a gascomponent density from the gas frequency component, and calculating thevoid fraction of gas as a ratio of the fluid component density minus theoverall density divided by the fluid component density minus the gascomponent density.

In yet another aspect of the meter electronics, the flow meter comprisesa Coriolis flow meter.

In one aspect of the method, the void fraction of gas comprises a voidfraction of air.

In another aspect of the method, receiving the frequency responsefurther comprises receiving a first sensor signal and a second sensorsignal from the flow meter, generating a ninety degree phase shift fromthe first sensor signal, and computing the frequency response using theninety degree phase shift.

In yet another aspect of the method, receiving the frequency responsefurther comprises receiving a first sensor signal and a second sensorsignal from the flow meter, generating a ninety degree phase shift fromthe first sensor signal, and computing the frequency response using thefirst sensor signal and the ninety degree phase shift.

In yet another aspect of the method, the breaking out comprisesprocessing the frequency response with one or more filters thatsubstantially reject one of the gas frequency component and the fluidfrequency component.

In yet another aspect of the method, the breaking out comprisesprocessing the frequency response with a notch filter that substantiallyrejects one of the gas frequency component and the fluid frequencycomponent.

In yet another aspect of the method, the breaking out comprisesfiltering the frequency response with a first filter that substantiallyrejects the gas frequency component and substantially passes the fluidfrequency component and filtering the frequency response with a secondfilter that substantially rejects the fluid frequency component andsubstantially passes the gas frequency component. The first filteroutputs the fluid frequency component and the second filter outputs thegas frequency component.

In yet another aspect of the method, the breaking out comprisesprocessing the frequency response with a low-pass filter, with alow-pass cut-off frequency of the low-pass filter being substantiallyabove the fluid frequency component, wherein the low-pass filtersubstantially passes the fluid frequency component and substantiallyrejects the gas frequency component, and processing the frequencyresponse with a high-pass filter, with a high-pass cut-off frequency ofthe high-pass filter being substantially below the gas frequencycomponent, wherein the high-pass filter substantially passes the gasfrequency component and substantially rejects the fluid frequencycomponent. The low-pass filter outputs the fluid frequency component andthe high-pass filter outputs the gas frequency component.

In yet another aspect of the method, the determining comprisescalculating an overall density from the frequency response, calculatinga fluid component density from the fluid frequency component,calculating a gas component density from the gas frequency component,and calculating the void fraction of gas as a ratio of the fluidcomponent density minus the overall density divided by the fluidcomponent density minus the gas component density.

In yet another aspect of the method, the flow meter comprises a Coriolisflow meter.

DESCRIPTION OF THE DRAWINGS

The same reference number represents the same element on all drawings.

FIG. 1 illustrates a Coriolis flow meter in an example of the invention;

FIG. 2 shows meter electronics according to an embodiment of theinvention.

FIG. 3 is a flowchart of a method of processing a sensor signal in aCoriolis flowmeter according to an embodiment of the invention.

FIG. 4 shows the meter electronics according to an embodiment of theinvention.

FIG. 5 is a flowchart of a method of processing first and second sensorsignals in a Coriolis flowmeter according to an embodiment of theinvention.

FIG. 6 is a block diagram of a portion of the processing systemaccording to an embodiment of the invention.

FIG. 7 shows detail of the Hilbert transform block according to anembodiment of the invention.

FIGS. 8 and 9 are block diagrams of two independent branches of theanalysis block according to an embodiment of the invention.

FIG. 10 is a power spectrum density plot of a pick-off sensor signal ofa flow meter under normal conditions.

FIG. 11 shows a Hilbert transform block according to the single phaseshift embodiment.

FIG. 12 shows the analysis block for the single phase shift embodiment.

FIG. 13 shows the sensor processing of the invention as compared to theprior art, wherein a time difference (Δt) value of each is compared.

FIG. 14 shows the meter electronics according to another embodiment ofthe invention.

FIG. 15 is a graph of flow meter frequency responses for air, for afluid, and for a combined air/fluid mix (i.e., for a fluid includingentrained air).

FIG. 16 is a flowchart of a method for determining a void fraction ofgas in a flow material flowing through a flow meter according to anembodiment of the invention.

FIG. 17 is a flowchart of a method for determining a void fraction ofgas in a flow material flowing through a flow meter according to anembodiment of the invention.

FIG. 18 is a frequency graph showing low-pass and high-pass filterresponses that can be used to break out a fluid frequency component anda gas frequency component according to an embodiment of the invention.

FIG. 19 is a flowchart of a method for determining a void fraction ofgas in a flow material flowing through a flow meter according to anembodiment of the invention.

FIG. 20 is a graph of a notch filter frequency response.

DETAILED DESCRIPTION OF THE INVENTION

FIGS. 1-20 and the following description depict specific examples toteach those skilled in the art how to make and use the best mode of theinvention. For the purpose of teaching inventive principles, someconventional aspects have been simplified or omitted. Those skilled inthe art will appreciate variations from these examples that fall withinthe scope of the invention. Those skilled in the art will appreciatethat the features described below can be combined in various ways toform multiple variations of the invention. As a result, the invention isnot limited to the specific examples described below, but only by theclaims and their equivalents.

FIG. 1 shows a Coriolis flow meter 5 comprising a meter assembly 10 andmeter electronics 20. Meter assembly 10 responds to mass flow rate anddensity of a process material. Meter electronics 20 is connected tometer assembly 10 via leads 100 to provide density, mass flow rate, andtemperature information over path 26, as well as other information notrelevant to the present invention. A Coriolis flow meter structure isdescribed although it is apparent to those skilled in the art that thepresent invention could be practiced as a vibrating tube densitometerwithout the additional measurement capability provided by a Coriolismass flow meter.

Meter assembly 10 includes a pair of manifolds 150 and 150′, flanges 103and 103′ having flange necks 110 and 110′, a pair of parallel flow tubes130 and 130′, drive mechanism 180, temperature sensor 190, and a pair ofvelocity sensors 170L and 170R. Flow tubes 130 and 130′ have twoessentially straight inlet legs 131 and 131′ and outlet legs 134 and134′ which converge towards each other at flow tube mounting blocks 120and 120′. Flow tubes 130 and 130′ bend at two symmetrical locationsalong their length and are essentially parallel throughout their length.Brace bars 140 and 140′ serve to define the axis W and W′ about whicheach flow tube oscillates.

The side legs 131, 131′ and 134, 134′ of flow tubes 130 and 130′ arefixedly attached to flow tube mounting blocks 120 and 120′ and theseblocks, in turn, are fixedly attached to manifolds 150 and 150′. Thisprovides a continuous closed material path through Coriolis meterassembly 10.

When flanges 103 and 103′, having holes 102 and 102′ are connected, viainlet end 104 and outlet end 104′ into a process line (not shown) whichcarries the process material that is being measured, material enters end104 of the meter through an orifice 101 in flange 103 is conductedthrough manifold 150 to flow tube mounting block 120 having a surface121. Within manifold 150 the material is divided and routed through flowtubes 130 and 130′. Upon exiting flow tubes 130 and 130′, the processmaterial is recombined in a single stream within manifold 150′ and isthereafter routed to exit end 104′ connected by flange 103′ having boltholes 102′ to the process line (not shown).

Flow tubes 130 and 130′ are selected and appropriately mounted to theflow tube mounting blocks 120 and 120′ so as to have substantially thesame mass distribution, moments of inertia and Young's modulus aboutbending axes W-W and W′-W′, respectively. These bending axes go throughbrace bars 140 and 140′. Inasmuch as the Young's modulus of the flowtubes change with temperature, and this change affects the calculationof flow and density, resistive temperature detector (RTD) 190 is mountedto flow tube 130′, to continuously measure the temperature of the flowtube. The temperature of the flow tube and hence the voltage appearingacross the RTD for a given current passing therethrough is governed bythe temperature of the material passing through the flow tube. Thetemperature dependent voltage appearing across the RTD is used in a wellknown method by meter electronics 20 to compensate for the change inelastic modulus of flow tubes 130 and 130′ due to any changes in flowtube temperature. The RTD is connected to meter electronics 20 by lead195.

Both flow tubes 130 and 130′ are driven by driver 180 in oppositedirections about their respective bending axes W and W′ and at what istermed the first out-of-phase bending mode of the flow meter. This drivemechanism 180 may comprise any one of many well known arrangements, suchas a magnet mounted to flow tube 130′ and an opposing coil mounted toflow tube 130 and through which an alternating current is passed forvibrating both flow tubes. A suitable drive signal is applied by meterelectronics 20, via lead 185, to drive mechanism 180.

Meter electronics 20 receives the RTD temperature signal on lead 195,and the left and right velocity signals appearing on leads 165L and165R, respectively. Meter electronics 20 produces the drive signalappearing on lead 185 to drive element 180 and vibrate tubes 130 and130′. Meter electronics 20 processes the left and right velocity signalsand the RTD signal to compute the mass flow rate and the density of thematerial passing through meter assembly 10. This information, along withother information, is applied by meter electronics 20 over path 26 toutilization means 29.

FIG. 2 shows meter electronics 20 according to an embodiment of theinvention. The meter electronics 20 can include an interface 201 and aprocessing system 203. The meter electronics 20 receives first andsecond sensor signals from the meter assembly 10, such aspickoff/velocity sensor signals. The meter electronics 20 processes thefirst and second sensor signals in order to obtain flow characteristicsof the flow material flowing through the meter assembly 10. For example,the meter electronics 20 can determine one or more of a phasedifference, a frequency, a time difference (Δt), a density, a mass flowrate, and a volume flow rate from the sensor signals, for example. Inaddition, other flow characteristics can be determined according to theinvention. The determinations are discussed below.

The phase difference determination and the frequency determination aremuch faster and more accurate and reliable than such determinations inthe prior art. In one embodiment, the phase difference determination andthe frequency determination are directly derived from a phase shift ofonly one sensor signal, without the need for any frequency referencesignal. This advantageously reduces the processing time required inorder to compute the flow characteristics. In another embodiment, thephase difference is derived from phase shifts of both sensor signals,while the frequency is derived from only one phase shift signal. Thisincreases the accuracy of both flow characteristics, and both can bedetermined much faster than in the prior art.

The prior art frequency determination methods typically take 1-2 secondsto perform. In contrast, the frequency determination according to theinvention can be performed in as little as 50 milliseconds (ms). Evenfaster frequency determination is contemplated, depending on the typeand configuration of the processing system, the sampling rate of thevibrational response, the filter sizes, the decimation rates, etc. Atthe 50 ms frequency determination rate, the meter electronics 20according to the invention can be about 40 times faster than the priorart.

The interface 201 receives the sensor signal from one of the velocitysensors 170L and 170R via the leads 100 of FIG. 1. The interface 201 canperform any necessary or desired signal conditioning, such as any mannerof formatting, amplification, buffering, etc. Alternatively, some or allof the signal conditioning can be performed in the processing system203.

In addition, the interface 201 can enable communications between themeter electronics 20 and external devices. The interface 201 can becapable of any manner of electronic, optical, or wireless communication.

The interface 201 in one embodiment is coupled with a digitizer 202,wherein the sensor signal comprises an analog sensor signal. Thedigitizer 202 samples and digitizes the analog sensor signal andproduces a digital sensor signal. The digitizer 202 can also perform anyneeded decimation, wherein the digital sensor signal is decimated inorder to reduce the amount of signal processing needed and to reduce theprocessing time. The decimation will be discussed in more detail below.

The processing system 203 conducts operations of the meter electronics20 and processes flow measurements from the flow meter assembly 10. Theprocessing system 203 executes one or more processing routines andthereby processes the flow measurements in order to produce one or moreflow characteristics.

The processing system 203 can comprise a general purpose computer, amicroprocessing system, a logic circuit, or some other general purposeor customized processing device. The processing system 203 can bedistributed among multiple processing devices. The processing system 203can include any manner of integral or independent electronic storagemedium, such as the storage system 204.

The processing system 203 processes the sensor signal 210 in order todetermine one or more flow characteristics from the sensor signal 210.The one or more flow characteristics can include a phase difference, afrequency, a time difference (Δt), a mass flow rate, and/or a densityfor the flow material, for example.

In the embodiment shown, the processing system 203 determines the flowcharacteristics from the two sensor signals 210 and 211 and the singlesensor signal phase shift 213. The processing system 203 can determineat least the phase difference and the frequency from the two sensorsignals 210 and 211 and the single phase shift 213. As a result, eithera first or second phase shifted sensor signal (such as one of theupstream or downstream pickoff signals) can be processed by theprocessing system 203 according to the invention in order to determine aphase difference, a frequency, a time difference (Δt), and/or a massflow rate for the flow material.

The storage system 204 can store flow meter parameters and data,software routines, constant values, and variable values. In oneembodiment, the storage system 204 includes routines that are executedby the processing system 203. In one embodiment, the storage system 204stores a phase shift routine 212, a phase difference routine 215, afrequency routine 216, a time difference (Δt) routine 217, and a flowcharacteristics routine 218.

In one embodiment, the storage system 204 stores variables used tooperate the Coriolis flow meter 5. The storage system 204 in oneembodiment stores variables such as the first sensor signal 210 and thesecond sensor signal 211, which are received from the velocity/pickoffsensors 170L and 170R. In addition, the storage system 204 can store a90 degree phase shift 213 that is generated in order to determine theflow characteristics.

In one embodiment, the storage system 204 stores one or more flowcharacteristics obtained from the flow measurements. The storage system204 in one embodiment stores flow characteristics such as a phasedifference 220, a frequency 221, a time difference (Δt) 222, a mass flowrate 223, a density 224, and a volume flow rate 225, all determined fromthe sensor signal 210.

The phase shift routine 212 performs a 90 degree phase shift on an inputsignal, i.e., on the sensor signal 210. The phase shift routine 212 inone embodiment implements a Hilbert transform (discussed below).

The phase difference routine 215 determines a phase difference using thesingle 90 degree phase shift 213. Additional information can also beused in order to compute the phase difference. The phase difference inone embodiment is computed from the first sensor signal 210, the secondsensor signal 211, and the 90 degree phase shift 213. The determinedphase difference can be stored in the phase difference 220 of thestorage system 204. The phase difference, when determined from the 90phase shift 213, can be calculated and obtained much faster than in theprior art. This can provide a critical difference in flow meterapplications having high flow rates or where multi-phase flows occur. Inaddition, the phase difference can be determined independent of thefrequency of either sensor signal 210 or 211. Moreover, because thephase difference is determined independently of the frequency, an errorcomponent in the phase difference does not include an error component ofthe frequency determination, i.e., there is no compounding error in thephase difference measurement. Consequently, the phase difference erroris reduced over a phase difference of the prior art.

The frequency routine 216 determines a frequency (such as that exhibitedby either the first sensor signal 210 or the second sensor signal 211)from the 90 degree phase shift 213. The determined frequency can bestored in the frequency 221 of the storage system 204. The frequency,when determined from the single 90 phase shift 213, can be calculatedand obtained much faster than in the prior art. This can provide acritical difference in flow meter applications having high flow rates orwhere multi-phase flows occur.

The time difference (Δt) routine 217 determines a time difference (Δt)between the first sensor signal 210 and the second sensor signal 211.The time difference (Δt) can be stored in the time difference (Δt) 222of the storage system 204. The time difference (Δt) comprisessubstantially the determined phase divided by the determined frequency,and is therefore used to determine the mass flow rate.

The flow characteristics routine 218 can determine one or more flowcharacteristics. The flow characteristics routine 218 can use thedetermined phase difference 220 and the determined frequency 221, forexample, in order to accomplish these additional flow characteristics.It should be understood that additional information may be required forthese determinations, such as the mass flow rate or density, forexample. The flow characteristics routine 218 can determine a mass flowrate from the time difference (Δt) 222, and therefore from the phasedifference 220 and the frequency 221. The formula for determining massflow rate is given in U.S. Pat. No. 5,027,662 to Titlow et al., and isincorporated herein by reference. The mass flow rate is related to themass flow of flow material in the meter assembly 10. Likewise, the flowcharacteristics routine 218 can also determine the density 224 and/orthe volume flow rate 225. The determined mass flow rate, density, andvolume flow rate can be stored in the mass flow rate 223, the density224, and the volume 225 of the storage system 204, respectively. Inaddition, the flow characteristics can be transmitted to externaldevices by the meter electronics 20.

FIG. 3 is a flowchart 300 of a method of processing sensor signals in aCoriolis flowmeter according to an embodiment of the invention. In step301, the first and second sensor signals are received. The first sensorsignal can comprise either an upstream or downstream pickoff sensorsignal.

In step 302, the sensor signals can be conditioned. In one embodiment,the conditioning can include filtering to remove noise and unwantedsignals. In one embodiment, the filtering can comprise band-passfiltering centered around the expected fundamental frequency of theCoriolis flow meter 5. In addition, other conditioning operations can beperformed, such as amplification, buffering, etc. If the sensor signalscomprise analog signals, the step can further comprise any manner ofsampling, digitization, and decimation that are performed in order toproduce digital sensor signals.

In step 303, a single 90 degree phase shift is generated. The 90 degreephase shift comprises a 90 degree phase shift of the sensor signal. The90 degree phase shift can be performed by any manner of phase shiftmechanism or operation. In one embodiment, the 90 degree phase shift isperformed using a Hilbert transform, operating on digital sensorsignals.

In step 304, a phase difference is computed, using the single 90 degreephase shift. Additional information can also be used in order to computethe phase difference. In one embodiment, the phase difference isdetermined from the first sensor signal, the second sensor signal, andthe single 90 degree phase shift. The phase difference comprises a phasedifference in the response signal, i.e., in a pickoff sensor, that isseen due to the Coriolis effect in the vibrating meter assembly 10.

The resulting phase difference is determined without the need for anyfrequency value in the calculation. The resulting phase difference canbe obtained much faster than a phase difference calculated using afrequency. The resulting phase difference has a greater accuracy than aphase difference calculated using a frequency.

In step 305, a frequency is computed. The frequency according to theinvention is advantageously computed from the 90 degree phase shift. Thefrequency in one embodiment uses the 90 degree phase shift and thecorresponding sensor signal from which the 90 degree phase shift isderived. The frequency is a vibrational response frequency of one of thefirst sensor signal and the second sensor signal (the frequencies of thetwo sensor signals are substantially identical in operation). Thefrequency comprises a vibrational frequency response of the flowtube orflowtubes to a vibration generated by the driver 180.

The frequency thus derived is obtained without the need for anyindependent frequency reference signal. The frequency is obtained fromthe single 90 degree phase shift in an operation that is much fasterthan in the prior art. The resulting frequency has a greater accuracythan a frequency calculated in the prior art.

In step 306, a mass flow rate of flow material is computed. The massflow rate is computed from the resulting phase difference and theresulting frequency computed in steps 304 and 305. In addition, the massflow rate computation can compute a time difference (Δt) from the phasedifference and the frequency, with the time difference (Δt) beingultimately used to compute the mass flow rate.

In step 307, the density can optionally be determined. The density canbe determined as one of the flow characteristics, and can be determinedfrom the frequency, for example.

In step 308, the volume flow rate can optionally be determined. Thevolume flow rate can be determined as one of the flow characteristics,and can be determined from the mass flow rate and the density, forexample.

FIG. 4 shows the meter electronics 20 according to an embodiment of theinvention. The elements in common with FIG. 2 share the same referencenumbers.

The meter electronics 20 in this embodiment includes the first sensorsignal 210 and the second sensor signal 211. The processing system 203processes the first and second (digital) sensor signals 210 and 211 inorder to determine one or more flow characteristics from the signals. Aspreviously discussed, the one or more flow characteristics can include aphase difference, a frequency, a time difference (Δt), a mass flow rate,a density, and/or a volume flow rate for the flow material.

In the embodiment shown, the processing system 203 determines the flowcharacteristics from only the two sensor signals 210 and 211, withoutthe need for any external frequency measurement and without the need foran external frequency reference signal. The processing system 203 candetermine at least the phase difference and the frequency from the twosensor signals 210 and 211.

As was previously discussed, the storage system 204 stores a phase shiftroutine 212, a phase difference routine 215, a frequency routine 216, atime difference (Δt) routine 217, and a flow characteristics routine218. The storage system 204 stores the first sensor signal 210 and thesecond sensor signal 211. The storage system 204 also stores a first 90degree phase shift 213 and a second 90 degree phase shift that aregenerated from the sensor signals in order to determine the flowcharacteristics. As was previously discussed, the storage system 204stores the phase difference 220, the frequency 221, the time difference(Δt) 222, the mass flow rate 223, the density 224, and the volume flowrate 225.

The phase shift routine 212 performs a 90 degree phase shift on an inputsignal, including on the first sensor signal 210 and on the secondsensor signal 211. The phase shift routine 212 in one embodimentimplements a Hilbert transform (discussed below).

The phase difference routine 215 determines a phase difference using thefirst 90 degree phase shift 213 and the second 90 degree phase shift214. Additional information can also be used in order to compute thephase difference. The phase difference in one embodiment is computedfrom the first sensor signal 210, the second sensor signal 211, thefirst 90 degree phase shift 212, and the second 90 degree phase shift213. The determined phase difference can be stored in the phasedifference 220 of the storage system 204, as previously discussed. Thephase difference, when determined using the first and second 90 phaseshifts, can be calculated and obtained much faster than in the priorart. This can provide a critical difference in flow meter applicationshaving high flow rates or where multi-phase flows occur. In addition,the phase difference can be determined independent of the frequency ofthe sensor signals 210 and 211. Moreover, because the phase differenceis determined independently of the frequency, an error component in thephase difference does not suffer from an error component of thefrequency determination, i.e., there is no compounding error in thephase difference measurement. Consequently, the phase difference erroris reduced over a phase difference of the prior art.

The frequency routine 216 determines a frequency (such as that exhibitedby either the first sensor signal 210 or the second sensor signal 211)from the first 90 degree phase shift 213 and the second 90 degree phaseshift 214. The determined frequency can be stored in the frequency 221of the storage system 204, as previously discussed. The frequency, whendetermined from the first and second 90 phase shifts, can be calculatedand obtained much faster than in the prior art. This can provide acritical difference in flow meter applications having high flow rates orwhere multi-phase flows occur.

The time difference (Δt) routine 217 determines a time difference (Δt)between the first sensor signal 210 and the second sensor signal 211.The time difference (Δt) can be stored in the time difference (Δt) 222of the storage system 204, as previously discussed. The time difference(Δt) comprises substantially the determined phase divided by thedetermined frequency, and is therefore used to determine the mass flowrate.

The flow characteristics routine 218 can determine one or more of themass flow rate, the density, and/or the volume flow rate, as previouslydiscussed.

FIG. 5 is a flowchart 500 of a method of processing first and secondsensor signals in a Coriolis flowmeter according to an embodiment of theinvention. In step 501, the first sensor signal is received. In oneembodiment, the first sensor signal comprises either an upstream ordownstream pickoff sensor signal.

In step 502, the second sensor signal is received. In one embodiment,the second sensor signal comprises either a downstream or upstreampickoff sensor signal (i.e., the opposite of the first sensor signal).

In step 503, the sensor signals can be conditioned. In one embodiment,the conditioning can include filtering to remove noise and unwantedsignals. In one embodiment, the filtering can comprise band-passfiltering, as previously discussed. In addition, other conditioningoperations can be performed, such as amplification, buffering, etc. Ifthe sensor signals comprise analog signals, the step can furthercomprise any manner of sampling, digitization, and decimation that areperformed in order to produce digital sensor signals.

In step 504, a first 90 degree phase shift is generated. The first 90degree phase shift comprises a 90 degree phase shift of the first sensorsignal. The 90 degree phase shift can be performed by any manner ofmechanism or operation. In one embodiment, the 90 degree phase shift isperformed using a Hilbert transform, operating on digital sensorsignals.

In step 505, a second 90 degree phase shift is generated. The second 90degree phase shift comprises a 90 degree phase shift of the secondsensor signal. As in the first 90 degree phase shift, the 90 degreephase shift can be performed by any manner of mechanism or operation.

In step 506, a phase difference is computed between the first sensorsignal and the second sensor signal, using the first 90 degree phaseshift and the second 90 degree phase shift. Additional information canalso be used in order to compute the phase difference. In oneembodiment, the phase difference is determined from the first sensorsignal, the second sensor signal, the first 90 degree phase shift, andthe second 90 degree phase shift. The phase difference comprises a phasedifference in the response signal, i.e., in the two pickoff sensors,that is seen due to the Coriolis effect in the vibrating meter assembly10.

The resulting phase difference is determined without the need for anyfrequency value in the calculation. The resulting phase difference canbe obtained much faster than a phase difference calculated using afrequency. The resulting phase difference has a greater accuracy than aphase difference calculated using a frequency.

In step 507, a frequency is computed. The frequency according to theinvention is advantageously computed from the first 90 degree phaseshift and the second 90 degree phase shift. The frequency in oneembodiment uses the 90 degree phase shift and the corresponding sensorsignal from which the 90 degree phase shift is derived. The frequency isa vibrational response frequency of one of the first sensor signal andthe second sensor signal (the frequencies of the two sensor signals aresubstantially identical in operation). The frequency comprises avibrational frequency response of the flowtube or flowtubes to avibration generated by the driver 180.

The frequency thus derived is obtained without the need for anyindependent frequency reference signal. The frequency is obtained fromthe 90 degree phase shifts in an operation that is much faster than inthe prior art. The resulting frequency has a greater accuracy than afrequency calculated in the prior art.

In step 508, a mass flow rate of flow material is computed. The massflow rate is computed from the resulting phase difference and theresulting frequency computed in steps 506 and 507. In addition, the massflow rate computation can compute a time difference (Δt) from the phasedifference and the frequency, with the time difference (Δt) beingultimately used to compute the mass flow rate.

In step 509, the density can optionally be determined, as previouslydiscussed.

In step 510, the volume flow rate can optionally be determined, aspreviously discussed.

FIG. 6 is a block diagram 600 of a portion of the processing system 203according to an embodiment of the invention. In the figure, the blocksrepresent either processing circuitry or processing actions/routines.The block diagram 600 includes a stage 1 filter block 601, a stage 2filter block 602, a Hilbert transform block 603, and an analysis block604. The LPO and RPO inputs comprise the left pickoff signal input andthe right pickoff signal input. Either the LPO or the RPO can comprise afirst sensor signal.

In one embodiment, the stage 1 filter block 601 and the stage 2 filterblock 602 comprise digital Finite Impulse Response (FIR) polyphasedecimation filters, implemented in the processing system 203. Thesefilters provide an optimal method for filtering and decimating one orboth sensor signals, with the filtering and decimating being performedat the same chronological time and at the same decimation rate.Alternatively, the stage 1 filter block 601 and the stage 2 filter block602 can comprise Infinite Impulse Response (IIR) filters or othersuitable digital filters or filter processes. However, it should beunderstood that other filtering processes and/or filtering embodimentsare contemplated and are within the scope of the description and claims.

FIG. 7 shows detail of the Hilbert transform block 603 according to anembodiment of the invention. In the embodiment shown, the Hilberttransform block 603 includes a LPO branch 700 and a RPO branch 710. TheLPO branch 700 includes a LPO delay block 701 in parallel with a LPOfilter block 702. Likewise, the RPO branch includes an RPO delay block711 in parallel with an RPO filter block 712. The LPO delay block 701and the RPO delay block 711 introduce sampling delays. The LPO delayblock 701 and the RPO delay block 711 therefore select LPO and RPOdigital signal samples that are chronologically later in time that theLPO and RPO digital signal samples that are filtered by the LPO filterblock 702 and the RPO filter block 712. The LPO filter block 702 and theRPO filter block 712 perform a 90 degree phase shift on the inputteddigital signal samples.

The Hilbert transform block 603 is a first step to providing the phasemeasurement. The Hilbert transform block 603 receives the filtered,decimated LPO and RPO signals and performs a Hilbert transform. TheHilbert transform produces 90 degree phase-shifted versions of the LPOand RPO signals, i.e., it produces quadrature (Q) components of theoriginal, in-phase (I) signal components. The output of the Hilberttransform block 603 therefore provides the new quadrature (Q) componentsLPO Q and RPO Q, along with the original, in-phase (I) signal componentsLPO I and RPO I.

The inputs to the Hilbert transform block 603 can be represented as:LPO=A _(lpo) cos(ωt)  (2)RPO=A _(rpo) cos(ωt+φ)  (3)Using the Hilbert transform the output becomes:LPO _(hilbert) =A _(lpo) sin(ωt)  (4)RPO _(hilbert) =A _(rpo) sin(ωt+φ)]  (5)Combining the original terms with the output of the Hilbert transformyields:LPO=A _(lpo)[cos(ωt)+i sin(ωt)]=A _(lpo) e ^(j(ωt))  (6)RPO=A _(rpo)[cos(ωt+φ)+i sin(ωt+φ)]=A _(rpo) e ^(j(ωt+φ))  (7)

FIGS. 8 and 9 are block diagrams of two independent branches of theanalysis block 604 according to an embodiment of the invention. Theanalysis block 604 is the final stage of the frequency, differentialphase, and delta T (Δt) measurement. FIG. 8 is phase portion 604 acomprising a first branch that determines a phase difference from thein-phase (I) and quadrature (Q) components. FIG. 9 is a frequencyportion 604 b that determines a frequency from the in-phase (I) andquadrature (Q) components of a single sensor signal. The single sensorsignal can comprise the LPO signal, as shown, or can alternativelycomprise the RPO signal.

In the embodiment of FIG. 8, the phase portion 604 a of the analysisblock 604 includes join blocks 801 a and 801 b, a conjugate block 802, acomplex multiplication block 803, a filter block 804, and a phase angleblock 805.

The join blocks 801 a and 801 b receive both in-phase (I) and quadrature(Q) components of a sensor signal and pass them on. The conjugate block802 performs a complex conjugate on a sensor signal (here the LPOsignal), and forms a negative of the imaginary signal. The complexmultiplication block 803 multiplies the RPO signal and the LPO signal,implementing equation (8) below. The filter block 804 implements adigital filter, such as the FIR filter discussed above. The filter block804 can comprise a polyphase decimation filter that is used to removeharmonic content from the in-phase (I) and quadrature (Q) components ofthe sensor signal, as well as to decimate the signal. The filtercoefficients can be chosen to provide decimation of the inputted signal,such as decimation by a factor of 10, for example. The phase angle block805 determines the phase angle from the in-phase (I) and quadrature (Q)components of the LPO signal and the RPO signal. The phase angle block805 implements equation (11) shown below.

The phase portion 604 a shown in FIG. 8 implements the followingequation:LPO×RPO=A _(lpo) e ^(−j(ωt)) ×A _(Rpo) e ^(j(ωt+φ)) =A _(lpo) ×A _(Rpo)e ^(j(−ωt+ωt+φ))  (8)where LPO is the complex conjugate of LPO. Assuming that:A_(Rpo)=A_(Lpo)=A  (9)then:LPO×RPO=A ² e ^(j(φ)) =A ²[cos(φ)+i sin(φ)]  (10)The resulting differential phase angle is:

$\begin{matrix}{\phi = {\tan^{- 1}\left\lbrack \frac{\sin(\phi)}{\cos(\phi)} \right\rbrack}} & (11)\end{matrix}$

FIG. 9 is a block diagram of a frequency portion 604 b of the analysisblock 604 according to the invention. The frequency portion 604 b canoperate on either the left or right pickoff signal (LPO or RPO). Thefrequency portion 604 b in the embodiment shown includes a join block901, a complex conjugate block 902, a sampling block 903, a complexmultiplication block 904, a filter block 905, a phase angle block 906, aconstant block 907, and a division block 908.

As previously discussed, the join block 901 receives both in-phase (I)and quadrature (Q) components of a sensor signal and passes them on. Theconjugate block 902 performs a complex conjugate on a sensor signal,here the LPO signal, and forms a negative of the imaginary signal. Thedelay block 903 introduces a sampling delay into the frequency portion604 b, and therefore selects a digital signal sample that ischronologically older in time. This older digital signal sample ismultiplied with the current digital signal in the complex multiplicationblock 904. The complex multiplication block 904 multiplies the LPOsignal and the LPO conjugate signal, implementing equation (12) below.The filter block 905 implements a digital filter, such as the FIR filterpreviously discussed The filter block 905 can comprise a polyphasedecimation filter that is used to remove harmonic content from thein-phase (I) and quadrature (Q) components of the sensor signal, as wellas to decimate the signal. The filter coefficients can be chosen toprovide decimation of the inputted signal, such as decimation by afactor of 10, for example. The phase angle block 906 determines a phaseangle from the in-phase (I) and quadrature (Q) components of the LPOsignal. The phase angle block 906 implements a portion of equation (13)below. The constant block 907 supplies a factor comprising a sample rateF_(s) divided by two pi, as shown in equation (14). The division block908 performs the division operation of equation (14).

The frequency portion 604 b implements the following equation:LPO _((n−1))×LPO _((n)) =A _(lpo) e ^(−j(ωt−1)) ×A _(Lpo) e ^(j(ωt)) =A² _(lpo) e ^(j(ωt−ωt) ⁻¹ ⁾  (12)The angle between two consecutive samples is therefore:

$\begin{matrix}{{{\omega\; t} - {\omega\; t_{- 1}}} = {\tan^{- 1}\left\lbrack \frac{\sin\left( {{\omega\; t} - {\omega\; t_{- 1}}} \right)}{\cos\left( {{\omega\; t} - {\omega\; t_{- 1}}} \right)} \right\rbrack}} & (13)\end{matrix}$which is the radian frequency of the left pick-off. Converting to Hz:

$\begin{matrix}{f_{lpo} = \frac{\left( {{\omega\; t} - {\omega\; t_{- 1}}} \right) \times {Fs}}{{2\;\pi}\;}} & (14)\end{matrix}$where “Fs” is the rate of the Hilbert transform block 603. In theexample previously discussed, “Fs” is about 2kHz.

FIG. 10 is a power spectrum density plot of a pick-off sensor signal ofa flow meter under normal conditions. The fundamental frequency of theflowmeter is the tallest spike of the graph and is located at about 135Hz. The figure also shows several other large spikes in the frequencyspectrum (the first non-fundamental mode is the twist mode at afrequency of about 1.5 times the frequency of the fundamental mode).These spikes comprise harmonic frequencies of the flowmeter and alsocomprise other, undesirable sensor modes (i.e., a twist mode, a secondbend mode, etc.).

FIG. 11 shows an alternative Hilbert transform block 603′ according to asingle phase shift embodiment. The Hilbert transform block 603′ in thisembodiment includes a LPO branch 1100 and a RPO branch 1110. The LPObranch 1100 includes a delay block 701 in parallel with a filter block702. The RPO branch 1110 in this embodiment includes only a delay block701. As before, the delay blocks 701 introduce sampling delays. Asbefore, the filter block 702 performs a 90 degree phase shift on theinputted digital signal sample. It should be understood thatalternatively the Hilbert transform block 603′ could phase shift justthe RPO signal.

This processing embodiment uses the Hilbert transform/phase shift ofonly one sensor signal in order to derive both the frequency and thephase difference (see FIGS. 2-3). This significantly reduces the numberof computations needed to perform a phase measurement and significantlyreduces the number of computations needed to obtain the mass flow rate.

In this embodiment, the output of the Hilbert transform block 603′ willprovide the quadrature (Q) component of either the left or right sensorsignal, but not both. In the example below, the LPO signal is phaseshifted.LPO=A _(lpo) cos(ωt)  (26)RPO=A _(rpo) cos(ωt+φ)  (27)Using the Hilbert transform, the output becomes:LPO _(hilbert) =A _(lpo) sin(ωt)  (28)RPO=A _(rpo) cos(ωt+φ)  (29)Combining the LPO original term with the output of the Hilbert transform(i.e., with the 90 phase shift) yields:LPO=A _(lpo)[cos(ωt)+i sin(ωt)]=A _(lpo) e ^(j(ωt))  (30)while the RPO stays the same:

$\begin{matrix}{{RPO} = {{A_{rpo}{\cos\left( {{\omega\; t} + \phi} \right)}} = {A_{rpo}\left\lbrack \frac{{\mathbb{e}}^{{j{({{\omega\; t} + \phi})}}\;} + {\mathbb{e}}^{- {j{({{\omega\; t} + \phi})}}}}{2} \right\rbrack}}} & (31)\end{matrix}$

FIG. 12 shows the analysis block 604 a′ for the single phase shiftembodiment. The analysis block 604 a′ in this embodiment includes onejoin block 801, the complex multiplication block 803, a low-pass filterblock 1201, and a phase angle block 805. The analysis block 604 a′ inthis embodiment implements the following equation:

$\begin{matrix}\begin{matrix}{{{LPO} \times {RPO}} = {A_{lpo}{\mathbb{e}}^{- {j{({\omega\; t})}}} \times {A_{rpo}\left\lbrack \frac{{\mathbb{e}}^{j{({{\omega\; t} + \phi})}} + {\mathbb{e}}^{- {j{({{\omega\; t} + \phi})}}}}{2} \right\rbrack}}} \\{= {\frac{A_{lpo} \times A_{Rpo}}{2}\left\lbrack {{\mathbb{e}}^{j{({{{- \omega}\; t} + {\omega\; t} + \phi})}} + {\mathbb{e}}^{j{({{\omega\; t} + {\omega\; t} + \phi})}}} \right\rbrack}}\end{matrix} & (32)\end{matrix}$

The low-pass filter block 1201 comprises a low-pass filter that removesa high-frequency component produced by the complex multiplication block803. The low-pass filter block 1201 can implement any manner of low-passfiltering operation. The result of the multiplication operation producestwo terms. The (−ωt+ωt+Ø) term combines and simplifies to a phase-only Øterm (a DC result), since the (−ωt) and the (ωt) terms cancel each otherout. The (ωt+ωt+Ø) simplifies to a (2ωt+Ø) term, at twice the frequency.Since the result is the sum of 2 terms, the high frequency (2ωt+Ø) termcan be removed. The only signal of interest here is the DC term. Thehigh frequency (2ωt+Ø) term can be filtered out of the result using alow-pass filter. The cut-off of the low-pass filter can be locatedanywhere between zero and 2ω.

After filtering, the result is:

$\begin{matrix}\begin{matrix}{{{LPO} \times {RPO}} = {A^{2}{\mathbb{e}}^{j{(\phi)}}}} \\{= {\frac{A^{2}}{2}\left\lbrack {{\cos(\phi)} + {{\mathbb{i}}\;{\sin(\phi)}}} \right\rbrack}}\end{matrix} & (33)\end{matrix}$Therefore, the differential phase angle is:

$\begin{matrix}{\phi = {\tan^{- 1}\left\lbrack \frac{\sin(\phi)}{\cos(\phi)} \right\rbrack}} & (34)\end{matrix}$

By taking the Hilbert transform of one pick-off signal instead of two,the computational load needed to perform phase and frequency estimationin Coriolis mass flow meters is advantageously reduced. The phase andfrequency can therefore be determined using two sensor signals, butusing only one 90 degree phase shift.

FIG. 13 shows the sensor processing of the invention as compared to theprior art, wherein a time difference (Δt) value of each is compared. Thechart shows a flow material including a gas flow (i.e., gas bubbles, forexample). Under this condition, the flow noise is substantially reducedin the new algorithm because of the rate of phase and frequencycalculation. It can be seen from the graph that the result derived bythe invention does not display the large peaks and valleys that arereflected in prior art (Δt) measurements.

FIG. 14 shows the meter electronics 20 according to another embodimentof the invention. The meter electronics 20 of this embodiment candetermine a void fraction of gas in a flow material flowing through anassociated flow meter, among other things. The meter electronics 20 canreceive a frequency response of the flow material, break out thefrequency response into at least a gas frequency component and a fluidfrequency component, and determine the void fraction of gas from thefrequency response and one or more of the gas frequency component andthe fluid frequency component. The void fraction can comprise asubstantially instantaneous void fraction. The meter electronics 20therefore can determine the flow characteristics of a fluid regardlessof the presence or amount of entrained gas.

The fluid can comprise any manner of fluid and the gas can comprise anymanner of gas. The gas can comprise air, for example. The discussionbelow focuses on air in a fluid, but it should be understood that theinvention applies to any gas.

The processing system 203 in this embodiment can include a void fractionroutine 1401, a notch filter routine 1402, and one or more filters orfilter routines, such as a low-pass filter routine 1403 and a high-passfilter routine 1404. Alternatively, the one or more filters or filterroutines can include a notch filter configuration or other filterconfiguration that rejects a narrow band of frequencies. The processingsystem 203 can further include a frequency response 1410 and a voidfraction 1418 that can store frequency response measurements and voidfraction determinations, respectively. The processing system 203 canfurther include a fluid frequency component 1416 and a gas frequencycomponent 1412 that store working frequency values for the void fractiondetermination. The processing system 203 can further include an overalldensity 1420, a gas component density 1421, and a fluid componentdensity 1422 that store working density values for the void fractiondetermination.

The frequency response 1410 in one embodiment comprises the previouslydiscussed frequency 221 received from the meter assembly 10 (see FIGS. 2and 4). The frequency response 1410 can be determined using thepreviously discussed processing blocks (see FIGS. 6-7 and 9).Advantageously, when using the previously discussed high-speed frequencydetermination, the invention can quickly, accurately, and reliablydetermine the void fraction of gas 1418.

In one embodiment, the frequency response 1410 is derived from first andsecond sensor signals, wherein the two sensor signals are processed bythe processing system 203 in order to obtain the frequency response1410. The processing can include phase shifting one sensor signal, aspreviously discussed, and generating frequency values based on thephase-shifted signal and the two sensor signals.

The frequency response 1410 comprises a mix frequency (f_(mix)), whereinthe frequency response 1410 can include an gas frequency component(f_(gas)) 1412 and a fluid frequency component (f_(fluid)) 1416. At anytime, the frequency response 1410 can include any amount of a gasfrequency component (f_(gas)) 1412 (i.e., entrained gas).

FIG. 15 is a graph of flow meter frequency responses for air, for afluid, and for a combined air/fluid mix (i.e., for a fluid includingentrained air). A basic concept of the invention is that the density ofa gas is distinguishable from the density of a fluid in the flowmaterial flowing through the flow meter. Since density can be derivedfrom a measured frequency that is obtained by a flow meter, thefrequency associated with air is also distinguishable from the frequencyof the fluid. This is also true of other gases or gas mixtures.

An equation for calculating frequency is:

$\begin{matrix}{{{\omega\; t} - {\omega\; t_{- 1}}} = {\tan^{- 1}\left\lbrack \frac{\sin\left( {{\omega\; t} - {\omega\; t_{- 1}}} \right)}{\cos\left( {{\omega\; t} - {\omega\; t_{- 1}}} \right)} \right\rbrack}} & (35)\end{matrix}$where ω is the radian frequency of the Coriolis flow meter. The ω⁻¹ termrepresents a radian frequency sample from a previous or earlier sampleperiod. Converting the radian frequency ω to a frequency f in Hertz (Hz)gives:

$\begin{matrix}{f_{fluid} = \frac{\left( {{\omega\; t} - {\omega\; t_{- 1}}} \right) \times F_{s}}{2\;\pi}} & (36)\end{matrix}$

This equation assumes only one frequency is present. If two frequenciesare present, as in the case of entrained air (the frequency of air andthe frequency of the flow material fluid), the new equation becomes:

$\begin{matrix}{f_{mix} = {\frac{F_{s}}{2\;\pi} \times \left( {\tan^{- 1}\left\lbrack \frac{{A_{fluid}^{2}{\sin\left( {{\omega_{fluid}t} - {w_{fluid}t_{- 1}}} \right)}} + {A_{air}^{2}{\sin\left( {{\omega_{air}t} - {\omega_{air}t_{- 1}}} \right)}}}{{A_{fluid}^{2}{\cos\left( {{\omega_{fluid}t} - {w_{fluid}t_{- 1}}} \right)}} + {A_{air}^{2}{\cos\left( {{\omega_{air}t} - {\omega_{air}t_{- 1}}} \right)}}} \right\rbrack} \right)}} & (37)\end{matrix}$where f_(mix) is the frequency response of the entire flow material,including a gas frequency component (f_(gas)) and a fluid frequencycomponent (f_(fluid)).

The low-pass filter routine 1403 implements a low-pass filter. Alow-pass filter passes low frequencies substantially below a low-passcut-off frequency. A low-pass filter therefore can be used to removehigh frequencies.

The high-pass filter routine 1404 implements a high-pass filter. Ahigh-pass filter passes high frequencies substantially above a high-passcut-off frequency. A high-pass filter therefore can be used to removelow frequencies.

The notch filter routine 1402 implements a notch filter. A notch filterrejects a narrow range of frequencies that are centered on a “notch” inthe frequency response of the notch filter. Only the frequencies in thenotch are rejected by the notch filter. Therefore, the notch filter isvery useful for removing known, undesired frequencies from the frequencyresponse 1410.

In operation, the meter electronics 20 receives the frequency response1410. The meter electronics 20 breaks out the frequency response 1410into the gas frequency component 1412 and the fluid frequency component1416. The meter electronics 20 uses the frequency response 1410 and oneor more of the gas frequency component 1412 and the fluid frequencycomponent 1416 to determine the void fraction of gas. The meterelectronics 20 determines an overall density (ρ_(mix)) 1420 from thefrequency response 1410. Likewise, a gas component density (ρ_(air))1421 is determined from the gas frequency component 1412 and a fluidcomponent density (ρ_(fluid)) 1422 is determined from the fluidfrequency component 1416 (see equations 38 and 39 below). These densityvalues can be used to determine the void fraction. Consequently, thevoid fraction can be determined for substantially any gas andsubstantially any liquid in the flow material.

Density (ρ) comprises:

$\begin{matrix}{\rho = {{m\left( \frac{1}{f} \right)}^{2} + b}} & (38)\end{matrix}$where m is the mass flow rate measurement, f is the frequencymeasurement, and b is some manner of calibration factor. Consequently,the void fraction of gas 1418 is calculated as a ratio of the fluidcomponent density (ρ_(fluid)) 1422 minus the overall density (ρ_(mix))1420 divided by the fluid component density (ρ_(fluid)) 1422 minus thegas component density (ρ_(gas)) 1421. The computation has the form:

$\begin{matrix}{{Void\_ Fraction} = \frac{\rho_{{fluid} -}\rho_{mix}}{\rho_{fluid} - \rho_{gas}}} & (39)\end{matrix}$

The resulting void fraction of gas 1418 reflects a ratio of gas to fluidin the flow material.

It should be understood that only one of the gas frequency component1412 and the fluid frequency component 1416 may be needed if either thegas or the fluid is known. For example, if the gas comprises air, then astandard air frequency response (and density) can be assumed. As aresult, the known gas or fluid frequency can be filtered out, and onlyone filtering step is needed.

The meter electronics 20 can additionally determine other flowcharacteristics, such as an overall mass flow rate, a mass flow rate ofjust the fluid component, a fluid density, etc. The meter electronics 20can be in communication with the meter assembly 10, where the meterassembly 10 can comprise any manner of flow meter that generates afrequency response. In one embodiment, the meter assembly 10 comprises aCoriolis flow meter. In another embodiment, the meter assembly 10comprises a vibrating densitometer.

It should be understood that the meter electronics 20 of this figure caninclude various other components and/or routines that were previouslydiscussed. Components and/or routines in common with other embodimentsshare common reference numbers. The meter electronics 20 can determine afrequency response and a density for the flow material as previouslydiscussed.

One method of breaking out the fluid and gas frequency components fromthe frequency response comprises performing two filtering operations.One filtering operation comprises filtering the frequency response witha first filter that substantially rejects the gas frequency componentand substantially passes the fluid frequency component. The secondfiltering operation comprises filtering the frequency response with asecond filter that substantially rejects the fluid frequency componentand substantially passes the gas frequency component. As a result, thefirst filter outputs the fluid frequency component and the second filteroutputs the gas frequency component.

FIG. 16 is a flowchart 1600 of a method for determining a void fractionof gas in a flow material flowing through a flow meter according to anembodiment of the invention. In step 1601, a frequency response isreceived. The frequency response can be received in the meterelectronics 20, for example. The frequency response comprises afrequency response to a vibrating meter assembly 10 that includes theflow material. The flow material can include entrained gas.

In one embodiment, the frequency response can comprise a first sensorsignal and a second sensor signal. The first sensor signal and thesecond sensor signal can be received from pick-off sensors 170L and 170Rof the meter assembly 10, for example. A 90 degree phase shift can begenerated from either sensor signal. The 90 degree phase shift and thefirst and second sensor signals can be used to compute the frequencyresponse, wherein the frequency response varies over time according toboth the mass flow rate of the flow material and according to thepresence and amount of entrained gas.

In step 1602, the frequency response is broken out into a gas frequencycomponent 1412 and a fluid frequency component 1416. This is possiblebecause the frequency response 1410 comprises a gas frequency componentthat is related to a gas flow rate in the flow material and a fluidfrequency component that is related to the fluid flow rate. The fluidcan comprise any manner of fluid. The breaking out can be performed by afirst filter and a second filter, as previously discussed. In addition,the breaking out can be performed by a low-pass filter and a high-passfilter, as previously discussed.

In step 1603, as previously discussed, the void fraction of gas 1418 isdetermined using the frequency response 1410, the gas frequencycomponent 1412, and the fluid frequency component 1416. Thedetermination can include determining density values from the frequencyresponse 1410, the gas frequency component 1412, and the fluid frequencycomponent 1416, as previously discussed. The resulting void fraction ofgas 1418 can be expressed as a ratio, a percentage, or other measure.

FIG. 17 is a flowchart 1700 of a method for determining a void fractionof gas in a flow material flowing through a flow meter according to anembodiment of the invention. In step 1701, a frequency response isreceived, as previously discussed.

In step 1702, the frequency response is filtered with a first filter.The first filter substantially rejects the gas frequency component andsubstantially passes the fluid frequency component (see FIG. 18). In oneembodiment, the first filter comprises a low-pass filter, wherein alow-pass cut-off frequency of the low-pass filter is substantially abovethe fluid frequency component. As a result, the low-pass filtersubstantially passes the fluid frequency component and substantiallyrejects the gas frequency component.

In step 1703, the frequency response is filtered with a second filter.The second filter substantially rejects the fluid frequency componentand substantially passes the gas frequency component. In one embodiment,the second filter comprises a high-pass filter, wherein a high-passcut-off frequency of the high-pass filter is substantially below the gasfrequency component (but above the fluid frequency component). As aresult, the high-pass filter substantially passes the gas frequencycomponent and substantially rejects the fluid frequency component.

In step 1704, as previously discussed, the void fraction of gas 1418 isdetermined using the frequency response 1410, the gas frequencycomponent 1412, and the fluid frequency component 1416.

FIG. 18 is a frequency graph showing low-pass and high-pass filterresponses that can be used to break out the fluid frequency componentand the gas frequency component according to an embodiment of theinvention. The lower line of the graph represents a flow meter frequencyresponse including a fluid frequency component lobe and a gas frequencycomponent lobe. The fluid frequency component lobe is lower in frequencythan the gas frequency component lobe. The upper lines comprise alow-pass filter response and a high-pass filter response, along with acut-off frequency. Here, the cut-off frequency for both the low-pass andhigh-pass filters is substantially centered between the two lobes. Thelow-pass and high-pass filters can have a common cut-off frequency orcan have different cut-off frequencies, depending on the fluid and gasfrequency components. It can be seen that the low-pass filter willoutput the fluid frequency component and the high-pass filter willoutput the gas frequency component. Therefore, the two filters can breakout the frequency response 1410 into the gas frequency component 1412and the fluid frequency component 1416.

Another method of breaking out the fluid and gas frequency componentscomprises filtering out a single, known frequency component and usingthe frequency component passed by the filter operation in order todetermine the fluid and gas component densities. For example, where gasin the flow material is air, then the filtering operation can beconfigured to filter out a relatively narrow frequency band centered ona typical air frequency response. Subsequently, the overall densityderived from the frequency response and the fluid density componentderived from the remaining fluid frequency component can be used todetermine an air density term. For example, where the gas is known to beatmospheric air, a filter (such as a notch filter, for example) can beused to substantially reject an air frequency component of the frequencyresponse. As a result, the overall density (ρ_(mix)) 1420 can becalculated from the frequency response 1410 and a fluid componentdensity (ρ_(fluid)) 1422 can be calculated from the fluid frequencycomponent 1416. Therefore, the air component density (ρ_(gas)) 1421comprises the overall density (ρ_(mix)) 1420 minus the fluid componentdensity (ρ_(fluid)) 1422.

Alternatively, it should be understood that the fluid frequencycomponent can be removed/filtered out, and the void fraction can bedetermined using the gas frequency component. As before, this singlefrequency removal can be performed where the fluid possesses a knowncharacteristic frequency response and density. Therefore, the singlefrequency removal method can remove either the fluid frequency componentor the gas frequency component.

In one embodiment, a single frequency component can be removed by one ormore filters while the other frequency component is passed by thefiltering operation. The one or more filters in one embodiment comprisea notch filter. A notch filter passes all frequencies except frequencieswithin a narrow band (i.e., a notch in the frequency response).Alternatively, the one or more filters can comprise any satisfactoryfilter or combination of filters.

FIG. 19 is a flowchart 1900 of a method for determining a void fractionof gas in a flow material flowing through a flow meter according to anembodiment of the invention. In step 1901, the frequency response 1410is received, as previously discussed.

In step 1902, the frequency response is processed with a notch filter.The notch filter passes frequencies above and below a notch, such asabove and below the gas frequency response in this embodiment.Therefore, the notch filter substantially rejects the gas frequencycomponent 1412. The notch filter substantially passes the fluidfrequency component 1416.

FIG. 20 is a graph of a notch filter frequency response. In the exampleshown, the notch is centered on a gas frequency. The notch filter passessubstantially all of the frequencies above and below the notch and onlythe gas frequency is substantially rejected by the notch filter.

In step 1903, the void fraction of gas 1418 is determined using thefrequency response, the gas frequency component 1412, and the fluidfrequency component 1416, as previously discussed.

The meter electronics and method according the invention can beimplemented according to any of the embodiments in order to obtainseveral advantages, if desired. The invention can determine a voidfraction of gas in a two phase flow. The invention can determine a voidfraction of gas in a multi-phase flow. The invention can determine avoid fraction of air. The invention can provide a void fraction of gasdetermination of greater accuracy and reliability. The invention canprovide a void fraction of gas determination faster than the prior artand while consuming less processing time.

1. Meter electronics (20) for determining a void fraction of gas in a flow material flowing through a flow meter (5), the meter electronics (20) comprising: an interface (201) for receiving a frequency response of the flow material; and a processing system (203) in communication with the interface (201) and configured to receive the frequency response from the interface (201), break out the frequency response into at least a gas frequency component and a fluid frequency component with one or more filters, and determine the void fraction of gas from the frequency response and one or more of the gas frequency component and the fluid frequency component.
 2. The meter electronics (20) of claim 1, with the void fraction of gas comprising a void fraction of air.
 3. The meter electronics (20) of claim 1, with the interface (201) including a digitizer (202) configured to digitize the frequency response.
 4. The meter electronics (20) of claim 1, with the processing system (203) being further configured to receive a first sensor signal and a second sensor signal from the flow meter (5), generate a ninety degree phase shift from the first sensor signal, and compute the frequency response using the ninety degree phase shift.
 5. The meter electronics (20) of claim 1, with the processing system (203) being further configured to receive a first sensor signal and a second sensor signal from the flow meter (5), generate a ninety degree phase shift from the first sensor signal, and compute the frequency response using the first sensor signal and the ninety degree phase shift.
 6. The meter electronics (20) of claim 1, with the one or more filters comprising a notch filter that substantially rejects one of the gas frequency component and the fluid frequency component.
 7. The meter electronics (20) of claim 1, with the processing system (203) being further configured to break out the frequency response by filtering the frequency response with a first filter of the one or more filters that substantially rejects the gas frequency component and substantially passes the fluid frequency component and filtering the frequency response with a second filter of the one or more filters that substantially rejects the fluid frequency component and substantially passes the gas frequency component, wherein the first filter outputs the fluid frequency component and the second filter outputs the gas frequency component.
 8. The meter electronics (20) of claim 1, with the processing system (203) being further configured to break out the frequency response by processing the frequency response with a low-pass filter of the one or more filters, with a low-pass cut-off frequency of the low-pass filter being substantially above the fluid frequency component and with the low-pass filter substantially passing the fluid frequency component and substantially rejecting the gas frequency component, and processing the frequency response with a high-pass filter of the one or more filters, with a high-pass cut-off frequency of the high-pass filter being substantially below the gas frequency component and with the high-pass filter substantially passing the gas frequency component and substantially rejecting the fluid frequency component, wherein the low-pass filter outputs the fluid frequency component and the high-pass filter outputs the gas frequency component.
 9. The meter electronics (20) of claim 1, with the processing system (203) being further configured to determine the void fraction of gas by calculating an overall density from the frequency response, calculating a fluid component density from the fluid frequency component, calculating a gas component density from the gas frequency component, and calculating the void fraction of gas as a ratio of the fluid component density minus the overall density divided by the fluid component density minus the gas component density.
 10. The meter electronics (20) of claim 1, with the flow meter (5) comprising a Coriolis flow meter (5).
 11. A method for determining a void fraction of gas in a flow material flowing through a flow meter, the method comprising: receiving a frequency response of the flow material in a meter electronics of the flow meter; the meter electronics breaking out the frequency response into at least a gas frequency component and a fluid frequency component with one or more filters; and the meter electronics determining the void fraction of gas from the frequency response and one or more of the gas frequency component and the fluid frequency component.
 12. The method of claim 11, with the void fraction of gas comprising a void fraction of air.
 13. The method of claim 11, with the receiving the frequency response further comprising: receiving a first sensor signal and a second sensor signal from the flow meter; generating a ninety degree phase shift from the first sensor signal; and computing the frequency response using the ninety degree phase shift.
 14. The method of claim 11, with the receiving the frequency response further comprising: receiving a first sensor signal and a second sensor signal from the flow meter; generating a ninety degree phase shift from the first sensor signal; and computing the frequency response using the first sensor signal and the ninety degree phase shift.
 15. The method of claim 11, with the one or more filters comprising a notch filter that substantially rejects one of the gas frequency component and the fluid frequency component.
 16. The method of claim 11, with the breaking out comprising: filtering the frequency response with a first filter of the one or more filters that substantially rejects the gas frequency component and substantially passes the fluid frequency component; and filtering the frequency response with a second filter of the one or more filters that substantially rejects the fluid frequency component and substantially passes the gas frequency component; wherein the first filter outputs the fluid frequency component and the second filter outputs the gas frequency component.
 17. The method of claim 11, with the breaking out comprising: processing the frequency response with a low-pass filter of the one or more filters, with a low-pass cut-off frequency of the low-pass filter being substantially above the fluid frequency component, wherein the low-pass filter substantially passes the fluid frequency component and substantially rejects the gas frequency component; and processing the frequency response with a high-pass filter of the one or more filters, with a high-pass cut-off frequency of the high-pass filter being substantially below the gas frequency component, wherein the high-pass filter substantially passes the gas frequency component and substantially rejects the fluid frequency component; wherein the low-pass filter outputs the fluid frequency component and the high-pass filter outputs the gas frequency component.
 18. The method of claim 11, with the determining comprising; calculating an overall density from the frequency response; calculating a fluid component density from the fluid frequency component; calculating a gas component density from the gas frequency component; and calculating the void fraction of gas as a ratio of the fluid component density minus the overall density divided by the fluid component density minus the gas component density.
 19. The method of claim 11, with the flow meter comprising a Coriolis flow meter.
 20. A method for determining a void fraction of gas in a flow material flowing through a flow meter, the method comprising: receiving a frequency response of the flow material in a meter electronics of the flow meter; the meter electronics processing the frequency response with a notch filter that substantially rejects one of a gas frequency component and a fluid frequency component; and the meter electronics determining the void fraction of gas from the frequency response and one or more of the gas frequency component and the fluid frequency component.
 21. The method of claim 20, with the void fraction of gas comprising a void fraction of air.
 22. The method of claim 20, with the receiving the frequency response further comprising: receiving a first sensor signal and a second sensor signal from the flow meter; generating a ninety degree phase shift from the first sensor signal; and computing the frequency response using the ninety degree phase shift.
 23. The method of claim 20, with the receiving the frequency response further comprising: receiving a first sensor signal and a second sensor signal from the flow meter; generating a ninety degree phase shift from the first sensor signal; and computing the frequency response using the first sensor signal and the ninety degree phase shift.
 24. The method of claim 20, with the determining comprising calculating an overall density from the frequency response; calculating a fluid component density from the fluid frequency component if the gas frequency component is rejected by the notch filter or calculating a gas component density if the fluid frequency component is rejected; estimating the gas component density if the gas frequency component is rejected by the notch filter or estimating the fluid component density if the fluid frequency component is rejected; calculating the void fraction of gas as a ratio of the fluid component density minus the overall density divided by the fluid component density minus the gas component density.
 25. The method of claim 20, with the flow meter comprising a Coriolis flow meter.
 26. A method for determining a void fraction of gas in a flow material flowing through a flow meter, the method comprising: receiving a frequency response of the flow material in a meter electronics of the flow meter; the meter electronics filtering the frequency response with a first filter that substantially rejects the gas frequency component and substantially passes the fluid frequency component, wherein the first filter outputs the fluid frequency component; the meter electronics filtering the frequency response with a second filter that substantially rejects the fluid frequency component and substantially passes the gas frequency component, wherein the second filter outputs the gas frequency component; the meter electronics determining the void fraction of gas from the frequency response and one or more of the gas frequency component and the fluid frequency component.
 27. The method of claim 26, with the void fraction of gas comprising a void fraction of air.
 28. The method of claim 26, with the receiving the frequency response further comprising: receiving a first sensor signal and a second sensor signal from the flow meter; generating a ninety degree phase shift from the first sensor signal; and computing the frequency response using the ninety degree phase shift.
 29. The method of claim 26, with the receiving the frequency response further comprising: receiving a first sensor signal and a second sensor signal from the flow meter; generating a ninety degree phase shift from the first sensor signal; and computing the frequency response using the first sensor signal and the ninety degree phase shift.
 30. The method of claim 26, with the determining comprising; calculating an overall density from the frequency response; calculating a fluid component density from the fluid frequency component; calculating a gas component density from the gas frequency component; and calculating the void fraction of gas as a ratio of the fluid component density minus the overall density divided by the fluid component density minus the gas component density.
 31. The method of claim 26, with the flow meter comprising a Coriolis flow meter.
 32. The method of claim 26, with the first filter comprising a low-pass filter and with the second filter comprising a high-pass filter. 